PPP Model Test - Assignment Example

Coefficients

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept

1.837

0.057

32.343

0.000

1.725

1.949

1.725

1.949

IDCt-IFCt

-4.794

5.659

-0.847

0.398

-15.992

6.403

-15.992

6.403

The regression equation is

ef = 1.837 - 4.794 (IDCt – IFCt).

(IDCt – IFCt) refers to the difference between the inflation rates of United States dollar less the inflation of the Turkish Lira. This implies an increase in the inflation of the Turkish Lira lowers the difference between the rates of inflation.

The coefficients in the model describe the kind of relationship that exists between the exchange rates and difference between the inflation rates. A negative coefficient shows that the dependent variable is negatively related to the indirectly related to inflation. This means that increase in the difference between the rates of inflation of the two currencies leads to a decrease in the exchange rates. The slope of the regression model is -4.794. This implies that an increase in the difference between the rates of inflation of the two currencies by one unit leads to a simultaneous decrease in the exchange rates by 4.794. (Wilson, Keating, & Beal, 2016).

An increase in the difference between the rates of inflation of the two currencies implies a decrease in the rates of inflation of the Turkish Lira. This means that a decrease in the inflation rate of the Turkish Lira leads to a decrease in the exchange rates. (Wilson, Keating, & Beal, 2016).

T test

We are bound to analyze the effectiveness of the regression model and thus the reliability of the results derived from the model. To achieve this, we test the significance of the regression model. The significance of the regression model is tested using the t-test which evaluates the relevance of variables in the model. The test uses;

The null hypothesis, Ho: βi=0

Alternative hypothesis, H1:βi≠0.

To test the hypothesis, we assume a level of significance of 0.05. The rejection region of the null hypothesis is p value < the level of significance. When the null hypothesis is less than the p value, it means that there exists sufficient statistical evidence to reject the null hypothesis. On the other hand, if there exists insufficient statistical evidence when the p value is > the level of significance. The rejection of the null hypothesis means that the independent variable is not significant in determining the dependent variable. The p value for the slope of the model is 0.398. The p value is therefore greater than the level of significance (0.398> 0.05). This means that there exists insufficient statistical evidence to reject the null hypothesis. We therefore fail to reject the null hypothesis and conclude that the relationship between the exchange rates and the difference between the inflations of the two currencies is insignificant. (Ivanova, 2007).

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept

1.837

0.057

32.343

0.000

1.725

1.949

1.725

1.949

IDCt - IFCt

-4.794

5.659

-0.847

0.398

-15.992

6.403

-15.992

6.403

The insignificance of the relationship means that as much as there exists a relationship between the exchange rates and the difference between the inflations of the two currencies, the impact of the difference between the inflations on the exchange rates is negligible. This suggests that there exists other factors that influence the exchange rates such that a single variable is not significantly related to the exchange rates.

F test

F test allows as to evaluate the prediction power of the model. The model test whether there exists a linear relationship between the variables. In this case, the F test evaluates whether there exists any significant linear relationship between the exchange rates and the difference between the inflation rates of the two currencies. The test use the following test;

Null hypothesis, H0: β = 0

Alternative hypothesis, H1: β ≠0.

ANOVA

df

SS

MS

F

Significance F

Regression

1

0.224417

0.224417

0.717684

0.398473586

Residual

129

40.33779

0.312696

Total

130

40.56221

To test the null hypothesis, we assume a level of significance of 0.05. The rejection region is p value < the level of significance. When the null hypothesis is less than the p value, it means that there exists sufficient statistical evidence to reject the null hypothesis. On the other hand, there exists insufficient statistical evidence when the p value is > the level of significance. The rejection of the null hypothesis means that the regression model has insignificant prediction value. The p value for the slope of the model is 0.3985. The p value is therefore greater than the level of significance (0.3985> 0.05). We therefore conclude that the model cannot be used for prediction of the future exchange rates as a result of fluctuations in the level of the difference in the inflations for the two currencies.

R squared

SUMMARY OUTPUT

Regression Statistics

Multiple R

0.074382

R Square

0.005533

Adjusted R Square

-0.00218

Standard Error

0.559192

Observations

131

The values of R squared explain the significance of the relationship between the dependent and the independent variables. The R squared is also called the coefficient of determination and is a value between 0 and 100%. The R squared is a percentage of the variance of response that is explained by the variance of the predictor. This measures the prediction ability and significance of the model. The value of R squared is 0.55%. This is low showing that the regression models is not appropriate for prediction. The forecast of the model would not be reliable meaning that the predicted values would be different from the actual values. (Ivanova, 2007).

The output below shows the predicted values and the residuals. The residuals represent the difference between the actual exchange rates and the predicted exchange rates. Large residual values represent the inaccuracy of the regression model used.

RESIDUAL OUTPUT

Observation

Predicted ef

Residuals

1

1.837852

-0.51315

2

1.823667

-0.48737

3

1.860344

-0.52564

4

1.903167

-0.46917

5

1.843658

-0.24086

6

1.863497

-0.3156

7

1.806555

-0.33816

8

1.922185

-0.43858

9

1.923882

-0.44888

10

1.906064

-0.44846

11

1.840985

-0.41028

12

1.870538

-0.44414

13

1.831865

-0.43447

14

1.837321

-0.42872

15

1.863712

-0.50411

16

1.831836

-0.49724

17

1.816114

-0.49661

18

1.803258

-0.52226

19

1.846877

-0.53028

20

1.873264

-0.61546

21

1.913695

-0.7121

22

1.901992

-0.71219

23

1.850811

-0.67091

24

1.851697

-0.6761

25

1.885118

-0.68922

26

1.84155

-0.59505

27

1.888372

-0.58907

28

1.868218

-0.62072

29

1.771418

-0.53622

30

1.839488

-0.62959

31

1.84446

-0.66276

32

1.865327

-0.62133

33

2.010173

-0.52417

34

1.968786

-0.37219

35

1.866991

-0.31899

36

1.829926

-0.22393

37

1.796816

-0.13312

38

1.878311

-0.16531

39

1.825965

-0.21757

40

1.853947

-0.29725

41

1.801151

-0.25445

42

1.856681

-0.33918

43

1.811949

-0.32195

44

1.85284

-0.36284

45

1.947955

-0.47405

46

1.894484

-0.39998

47

1.870871

-0.36277

48

1.909308

-0.43641

49

1.905261

-0.38606

50

1.845324

-0.31102

51

1.857334

-0.36613

52

1.816154

-0.26435

53

1.814799

-0.237

54

1.813016

-0.27622

55

1.849747

-0.33845

56

1.893072

-0.40137

57

1.918893

-0.49419

58

1.836343

-0.38974

59

1.814355

-0.29276

60

1.833983

-0.26768

61

1.848324

-0.25892

62

1.810366

-0.23237

63

1.847708

-0.32541

64

1.930557

-0.35516

65

1.773584

-0.17188

66

1.813171

-0.15417

67

1.858635

-0.10064

68

1.865853

-0.06565

69

2.003815

-0.17452

70

1.923888

-0.10799

71

1.876481

-0.00428

72

1.842924

-0.00382

73

1.842997

-0.0855

74

1.820464

-0.02936

75

1.895196

-0.1079

76

1.832486

-0.02419

77

1.801147

0.020753

78

1.833854

-0.02215

79

1.837119

-0.03952

80

1.865133

-0.06453

81

1.93293

-0.13033

82

1.877887

-0.08509

83

1.868239

-0.08084

84

1.901791

-0.13129

85

1.81216

-0.03376

86

1.856271

-0.04757

87

1.862188

-0.06579

88

1.835489

-0.00909

89

1.862142

0.038458

90

1.850077

0.083823

91

1.826323

0.136477

92

1.86815

0.14885

93

1.935687

0.048913

94

1.847259

0.177241

95

1.859539

0.203461

96

1.914051

0.309049

97

1.839845

0.367655

98

1.860136

0.353264

99

1.885724

0.239776

100

1.839254

0.250846

101

1.843019

0.275181

102

1.860704

0.258896

103

1.84959

0.31251

104

1.840136

0.374964

105

1.940166

0.311034

106

1.871619

0.361381

107

1.843036

0.451364

108

1.912447

0.422853

109

1.850489

0.615411

110

1.865344

0.728956

111

1.905447

0.752053

112

1.839595

0.808005

113

1.79562

0.90428

114

1.840977

0.860123

115

1.863032

0.996068

116

1.887349

1.128151

117

1.913732

1.010668

118

1.879104

0.997496

119

1.863412

1.059188

120

1.916282

1.096118

121

1.83205

1.11145

122

1.814481

1.070319

123

1.851898

0.981702

124

1.845402

1.093098

125

1.843891

1.068109

126

1.90059

1.06981

127

1.818729

1.140771

128

1.8342

1.1354

129

1.90003

1.17847

130

1.869286

1.429314

131

1.91427

1.58383

The high residual values depict the unreliability of the predictions made by the model. The low prediction power is an indication that there other factors that influence the exchange rates other than the difference of the inflation rates of the two currencies. It would be therefore more appropriate to use a multivariate regression analysis that would ably include the effect of multiple factors influencing the exchange rates simultaneously. The simple linear regression model derived is not useful for prediction. It however analyses the relationship between the two variables. The graph below gives a clear impression of how the predicted values of the exchange rates differ from the actual exchange rates.

Scatter plot

The graph below shows the plots of the observation of the exchange rates made against the difference sin the rates of inflation of the two currencies. The scatter shows no linear relationship since the observations are not evenly distributed. This explains the reasons why the model’s prediction power is low.

Hypothesis

Null hypothesis H0: α=0.

Alternative hypothesis H0: α0.

The null hypothesis implies that the intercept in the regression model is zero. The intercept is equal to the exchange rate when the difference between the inflation rates of the two currencies is zero.

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept

1.837

0.057

32.343

0.000

1.725

1.949

1.725

1.949

IDCt- IFCt

-4.794

5.659

-0.847

0.398

-15.992

6.403

-15.992

6.403

To evaluate whether to reject or accept the null hypothesis, we assume a level of significance of 0.05. The rejection region is p value < the level of significance. When the null hypothesis is less than the p value, it means that there exists sufficient statistical evidence to reject the null hypothesis. On the other hand, there exists insufficient statistical evidence when the p value is > the level of significance. The p value is 0.000. This implies that p value is less than the level of significance. We therefore reject the null hypothesis and conclude that the y intercept is not equal to zero, meaning that the value of the exchange rate is not zero when the inflations of the currencies are equal. (Cane-Honeysett, 2017).

Null hypothesis: H0: β=1

Alternative hypothesis: H0: β=1.

The null hypothesis implies that the value of the slope is 1 unit meaning that an increase in the differences between the inflations by one unit increases the rates of exchange by 1 unit.

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept

1.837

0.057

32.343

0.000

1.725

1.949

1.725

1.949

IDCt- IFCt

-4.794

5.659

-0.847

0.398

-15.992

6.403

-15.992

6.403

To evaluate whether to reject or accept the null hypothesis, we assume a level of significance of 0.05. The rejection region is p value < the level of significance. When the null hypothesis is less than the p value, it means that there exists sufficient statistical evidence to reject the null hypothesis. On the other hand, there exists insufficient statistical evidence when the p value is > the level of significance. We can also use the t tables to evaluate whether to reject or accept the null hypothesis. To use the tables, we evaluate critical value of t. (Cane-Honeysett, 2017).

t= coefficient – hypothesized / standard error = (-4.794 -1)/ 5.659 = -1.02385

We use the t tables to find the critical value t 0.025, 128 = 1.962.

The rejection region occurs if the t computed < the critical value. We therefore reject the null hypothesis and conclude that the null hypothesis is not true.

We can also use statistical software to establish the p value. And then use it to decide whether to accept or reject the null hypothesis. Using technology, the two-tailed P value equals 0.3079. This is greater than the level of significance, 0.05. We therefore reject the null hypothesis and conclude that the slope coefficient is not equal to one. This means that if the difference between the inflation rates of the two currencies is increases by 1 unit, the exchange rate changes by more than one unit. The changes are not equivalent.

Findings

The research concludes that the relationship between the difference between the inflation of the Turkish lira and the US dollar has an impact on the exchange rates levels’. The impact is however not significant. This implies that there are several factors that influence the exchange rates. The factors that influence the exchange rates include;

Differentials in inflation

Inflation is the uncontrolled increase in the prices of commodities. An economy with a low rate of inflation has a more stable currency due to its high purchasing power. On the other hand, increase in the rate of inflation means reduced purchasing power of a currency. High inflation induce depreciation of a currency while the reduced inflation cause the currency to appreciate. (Douglas, Lovrencic, & Pontikis, 2011).

Differentials in the interest rates

Interest rates are determined by the forces of aggregate demand and supply. The central bank regulates the interest rates to establish stability in the economy because of interest rates influence on the rate of inflation. High interest rates in an economy provide lenders with high rate of return. This increases the amount of foreign investment in an economy and therefore leads to increase in exchange rates.

Balance of trade

Balance of trade includes all the payments made between a country and foreign countries. When a country has a deficit, it means that the country purchases more than the amount earned from foreign countries. A deficit means that a country requires more foreign currency and thus depreciation of its currency.

Debt

When country has a large debt, it means that there is deficit in its financing. Large public and foreign debts induce inflation and are as a result not attractive to investors. This leads to depreciation of the country’s currency. The effect of debt on the exchange rates is even worse if a country is forced to print more money to repay debt. This increases money supply and hence high rates of inflation that may lead to further depreciation. (Douglas, Lovrencic, & Pontikis, 2011).

Terms of trade

Terms of trade is a ratio that compares the export to import prices, when the prices of exports are high as compared to the prices of imports. A high terms of trade improves the balance of trade given that it means more priced exports than imports. A favorable balance of trade result in to appreciation of the currency.

Economic performance and political stability

Political stability in a country attract foreign investors into a country. Peace is an important factor for business to perform well. The economic performance of a country may also attract or repel investors. The more the number of foreign investors, the more the reserves of foreign countries that a currency develops. A large reserve of foreign currency in turn causes appreciation of the domestic currency. (Douglas, Lovrencic, & Pontikis, 2011).

The regression model would be more informative if a multivariate analysis approach including all more factors influencing the exchange rate was used rather than one variable.